How much time is remaining?

Excel, 6 Bytes

=B1-A1

Assuming A is in cell A1 and B is in cell B1

MATL, 17 7 bytes

YOd15XO

Input is a cell array of strings, in the form {'1:45' '3:15'} or {'1:45', '3:15'}.

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Explanation

YO     % Input cell array of strings (implicit). Convert to serial date numbers
d      % Difference
15XO   % Convert to format 15, i.e. 'HH:MM'. Display (implicit)

Bash + coreutils, 44 39 bytes

tr : \ |dc -e?r60*+r-r60*-60~rn58PA~rnn

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Explanation: using "1:45 3:15" as test case (last example). I show intermediary steps in quotes.

tr : \ |         # replace colons with spaces: "1 45 3 15"
dc -e?           # start dc script, push input to LIFO stack: "15 3 45 1"
     r60*+            # turn time B to total seconds: "195 45 1"
     r-r60*-          # turn time A to total seconds and get difference: "90"
     60~r             # turn difference (time left) to minutes and seconds: "1 30"
     n58P             # pop and print minutes, print colon (ASCII code 58): "30"
     A~rnn            # print seconds. Padding with zeroes is done by dividing by
                      #10 (A), and printing the quotient and the remainder.

Note that I don't check if the minute value needs zero padding, because the OP stated that the maximum value for m is 9.

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Below is my original 44 bytes answer, that used the date command to turn the total time left in seconds to the m:ss format.

date -d@`tr : \ |dc -e?r60*+r-r60*-p` +%M:%S